Counterparty risk: credit valuation adjustment variability and value-at-risk

Abstract

The third installment of the Basel Accords advocates a capital charge against credit valuation adjustment (CVA) variability. We propose an efficient numerical approach that allows us to compute risk measures for the CVA process by assessing the distribution of the CVA at a given horizon. This approach relies on a recursive formulation of the CVA, yielding the adjustment as a function of both the time to maturity and the value of the risk factors. Numerical experiments are presented to illustrate the impact of various parameters and assumptions on the CVA distribution. More specifically, we investigate the impact of the constant exposure approximation and show that this assumption significantly affects the tail of the distribution of CVA movements. We also find that distortions between physical and risk-neutral probability measures have practically no impact on the dispersion of the CVA distribution. Finally, we analyze the effect of wrong-way risk and of early exercise opportunities on the evaluation of risk measures.